y 1 



UNIVERSITY OF ILLINOIS BULLETIN 

Issued Weekly 
Vol. XIX July 3, 1922 . No. 45 

[Entered as second-class matter December ii, 1912, at the post office at Urbana, Illinois, under the 
Act of August 24, 1912. Acceptance for mailing at the special rate of postage provided for in 
section 1103, Act of October 3, 1917, authorized July 31, 1918.] 



BULLETIN NO. 10 

BUREAU OF EDUCATIONAL RESEARCH 
COLLEGE OF EDUCATION 



RELATION OF SIZE OF GLASS TO 
SCHOOL EFFICIENCY 

Bureau of Educational Research 

Prepared, in part, from a report by P. R. Stevenson, 

former Assistant, Bureau of Educational Research. 




PRICE 50 CENTS 



PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA 

1922 



m 






BULLETIN NO. 10 

BUREAU OF EDUCATIONAL RESEARCH 
COLLEGE OF EDUCATION 



RELATION OF SIZE OF GLASS TO 
SCHOOL EFFICIENCY 

by 
Bureau of Educational Research 

Prepared, in part, from a report by P. R. Stevenson, 
former Assistant, Bureau of Educational Research. 



PRICE SO CENTS 



PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA 

1922 



V. 



TABLE OF CONTENTS 



PAGE 

Preface 3 

I. Introduction: Relation of Size of Class to School 

Efficiency 5 

11. Existing Conditions in Regard to Class Size 10 

III. Relation of Size of Class in Elementary School to 

School Efficiency 16 

IV. Relation of Size of Class in High School to School 

Efficiency 24 

V. Suggestions for Educational Experimentation 37 



IlBKARY OF CONGH^^SS 






PREFACE 



This investigation was initiated by Mr. B. R. Buckingham, 
formerly Director of the Bureau of Educational Research. It was 
planned and executed by him with the assistance of Mr. P. R. Steven- 
son, a full time assistant in the employ of the Bureau of Educational 
Research during the school year of 1920-21. The present Director 
of the Bureau of Educational Research had no connection with the 
study until late in the summer of 1920-21. The portion of this 
report which deals with "existing conditions in regard to class size" 
and "the relation of size of class in high schools to school efficiency" 
is based upon tabulations made by employees of the Bureau of 
Educational Research under Mr, Stevenson's direction and included 
by him in a report submitted to the present Director of the Bureau 
of Educational Research. The chapter devoted to the relation of 
the size of class In elementary schools to school efficiency Is based 
upon tabulations made from the original data under the Immediate 
direction of the present Director. The concept of the efficiency 
ratio and the use of this concept in the Interpretation of the data 
are entirely the work of the present Director of the Bureau of Edu- 
cational Research. The conclusions are also his own. 

Certain limitations of the investigation, which the report dis- 
cusses in detail, cause the results to have a limited practical signifi- 
cance, but it is thought that the publication Is juslfied for two rea- 
sons. In the first place, the concept of school efficiency and the 
analysis of the conditions which must be considered in any investi- 
gation relating to school efficiency should be helpful to future Inves- 
tigators not only of the question of class size but also of questions 
of other phases of school procedure. In the second place, the report 
emphasizes the need for careful planning which will result In the 
control of all factors involved In the teaching situation. There Is 
also emphasis upon the need for securing normal conditions If the 
results are to be interpreted with reference to the modification of 
practise. Such analysis and careful thinking are not only important 
phases of educational research but they are the foundation upon 
which both the data collected and the statistical manipulation of them 
are based. 



This investigation was made possible through the cooperation 
of Superintendent Peter A. Mortenson, of the Chicago Public Schools, 
and of the school officials in certain other Illinois cities. Not only 
did they cooperate by permitting the collection of the data, but they 
actually made substantial contributions to the project by furnishing 
the test materials. The teachers in the schools concerned made a 
substantial contribution by scoring the tests and reporting them in 
a convenient form to the Bureau of Educational Research. The 
writer is glad to acknowledge the indebtedness of the Bureau of 
Educational Research to all those who have contributed to the 
project. 

Walter S. Monroe, Director. 
May 26, 1922. 



RELATION OF SIZE OF CLASS TO SCHOOL EFFICIENCY 

CHAPTER I 
INTRODUCTION: ANALYSIS OF PROBLEM 

The problem. The problem of this investigation is to study 
the relation of the size of class to school efficiency, or what is the 
effect upon the efficiency of the school when the size of class is in- 
creased or decreased within certain limits. 

Definition of terms: Class. In the high school, a class is de- 
fined as the number of pupils who are assigned to a single teacher 
for instruction during a single class period. In the elementary school, 
unless the instruction has been departmentalized, a class is the 
number of pupils assigned to a room over which a teacher has charge. 
For instructional purposes, a teacher in the elementary school may 
divide a class into two or three groups, but the total number of 
pupils receiving instruction from her is considered a class, as the 
term is used in this study. 

School efficiency. Educators have borrowed the term "effi- 
ciency" from industry and business. In these fields, efficiency is 
expressed by a fraction whose maximum is 1.00. The numerator 
of this fraction, or "efficiency ratio," is the output, and the denom- 
inator is the input, or educational investment. In education, the 
output of a school system consists of the changes produced in the 
pupils, i. e., the controls of conduct that the school engenders. The 
educational output for a semester or a year is the total of all the 
changes that have been produced in the pupils during the period due 
to the influence of the school. The educational investment includes 
many factors, such as buildings, equipment, textbooks, teachers, 
supervision, and general administration. Although it is not imper- 
ative to do so, it is probably best to think of both the output and the 
investment as being expressed in terms of the average for one pupil. 

We are accustomed to refer to the educational output as the 
achievements of the pupils. By means of educational tests and 
other instruments, we measure these achievements in terms of arbi- 
trary units. Units of one type are implied in school marks. Other 



units are defined by educational tests. In order to calculate the 
numerical value of the efficiency ratio, it would be necessary to de- 
termine the social value of the output in terms of dollars and cents 
or in terms of some unit which might be made common to both 
numerator and denominator. Obviously, we are not prepared to do 
this. However, we may use the ratio as a definition of school effi- 
ciency and inquire into the probable nature of the changes produced 
in it by the variations of certain factors upon which the educational 
output and educational investment depend. In making inferences 
concerning the fluctuations in the value of the efficiency ratio, it is 
necessary to remember that the production of certain achievements 
may be of little value when viewed in relation to our educational 
objectives. The attainment of certain levels of achievement may 
represent an educational output of considerable value, but advance- 
ment to higher levels may produce only slight increases in the value 
of the total output in this field. For example, the attainment of 
certain levels of ability in spelling has a distinct and relatively large 
social value, but advancement beyond these levels is accompanied 
by rapidly diminishing increments of value. Therefore, one must 
avoid the assumption that fluctuations in achievements are to be 
interpreted as having proportional values in terms of social worth. 

Factors which affect school efficiency. For a given educa- 
tional investment per pupil, the value of the efficiency ratio is af- 
fected when changes are made in the educational output. Methods 
of instruction, the plan of school organization, or the procedure of 
supervision may be modified even when there is no change in the 
investment. When modifications in the methods of using the in- 
vestment result in changes in the educational output, there are re- 
sulting changes in the value of the efficiency ratio. On the other 
hand, it is possible that material changes may be made in the educa- 
tional investment which are not accompanied by corresponding 
changes in the educational output. When this happens, the value 
of the efficiency ratio is changed, even though the actual educational 
output has remained constant. 

In many cases, modifications in the method of using the educa- 
tional investment are accompanied by changes in the magnitude of the 
educational investment as well as by changes in the educational output. 
Hence, we may have fluctuations occurring in both the numerator 



and the denominator of the efficiency ratio. It is possible that these 
fluctuations may be connected in such a way that the value of the 
efficiency ratio remains constant, or it may be that its magnitude 
will vary. Because we are not able to calculate a numerical value 
of the efficiency ratio, a careful analysis is required to determine 
the probable changes in it when variations occur in the numerator 
and the denominator simultaneously. 

The achievements of pupils are materially affected by their 
general intelligence or capacity to learn. Since individual pupils and 
also groups of pupils have been shown to exhibit marked individual 
differences when measured with respect to this trait, it is necessary 
to make due allowance for differences in general intelligence when 
comparing different school units with respect to efficiency. In case 
this is not done an error of interpretation will be made by attrib- 
uting a higher degree of efficiency to those units which consist of 
pupils of superior general intelligence. 

The effect of varying tlie size of class. The size of class is 
one item of the plan of the organization. From this point of view, 
it may be considered one of the methods of using the educational 
investment. Consequently, we may expect to find that changes in 
the size of class produce variations in the achievements of pupils. 
The size of the class is, also, one of the factors which determines the 
educational investment. In the elementary school, where a class 
means the number of pupils assigned to a teacher, the cost of in- 
struction per pupil varies inversely with the size of class.^ In a high 
school the size of class does not completely determine the number 
of student hours of instruction which a teacher gives, but it is a 
potent factor in this determination. In general, an increase in the 
size of class in the high school will tend to result in a marked de- 
crease in the educational investment per pupil. Hence, in studying 
the effect of varying the size of class upon the efficiency of the school, 
it is necessary for us to inquire into the resulting changes in both 
the educational output and the educational investment. It is only 
when we have done this that we are in a position to make inferences 
concerning the effect of variations in the size of class upon the effi- 
ciency of the school. 

*In making this statement, no account is taken of investments made in super- 
vision, in instruction by special teachers, and in equipment. 



The practical importance of a study of the relation of class 
size to school efficiency. During recent years, school adminis- 
trators have faced the problem of providing instruction for a rap- 
idly increasing enrollment and, at the same time, of meeting the 
demands from teachers for increased salaries. In meeting these two 
demands, there has been a tendency to increase the number of 
pupils instructed by a teacher in order to keep the total educational 
expenditure within the income of the school system. In the elemen- 
tary school, and to a considerable extent in the high school, the 
number of pupils instructed by a teacher has been increased by 
increasing the size of classes. It is obvious that pupils in large 
classes have less opportunity for recitation and, in general, receive 
less Individual attention from the teacher, both within and outside 
of the class period. Thus, the question has naturally been raised 
concerning the effect upon the efficiency of a school when the size 
of the class is increased. In the secondary school added emphasis is 
given to the question because certain accrediting agencies require 
that the size of the class not exceed a certain fixed maximum. 

Connection between size of class and methods of instruc- 
tion. It is necessary to bear in mind that, when the number of 
pupils instructed by a teacher is increased, there is a corresponding 
increase in the amount of work required of the teacher, unless there 
are compensating changes in the methods of instruction. For ex- 
ample, according to our present methods, it is customary to require 
a great deal of written work of pupils studying English composition. 
A teacher is expected to read with considerable care the composi- 
tions submitted by pupils and to provide a systematic procedure for 
correcting the errors made. Thus, an increase in the number of 
pupils to be taught increases the work required of the teacher un- 
less the number of compositions required from each pupil is reduced 
or a different system of handling them is used. Much the same 
conditions prevail in a number of other subjects in which notebooks 
or other written work of some sort are customarily required. Sim- 
ilar statements can be made with reference to individual work with 
pupils outside of the regular class period. It is obvious that there is 
a limit to the amount of work which may legitimately be required 
of a teacher. When the optimal teaching load has been reached, 
any increase in the number of pupils assigned to a teacher should 



be expected to be accompanied by compensating changes in the pro- 
cedure of instruction. When such changes are made in the teaching 
procedure, they, as well as the size of the class, must be considered 
in respect to the effect upon the efficiency of the school. 

Limitations of the present investigation. In this investiga- 
tion of the effect of varying the size of class upon school efficiency, 
it was intended that all other factors which affect either the achieve- 
ments of pupils or the educational investment should be kept con- 
stant, i. e., they should be the same for classes of different sizes. 
No information is available to show the extent to which this inten- 
tion was realized except in the case of the quality of the pupil ma- 
terial. Group intelligence tests were used to secure equivalence of 
capacity to learn in the two groups of pupils. The possibility of a 
lack of equivalence of such factors as home environment, nation- 
ality, attitude toward school work, previous school experience with 
respect to size of class, time of day (applies only to high school), 
etc., makes it necessary to exercise due caution in interpreting the 
results of the investigation. 

So far as the present writer is aware, the instruction that pre- 
vailed in the groups concerned in this investigation involved no un- 
usual features, and the same methods of instruction were followed 
in the two types of classes. It is possible that the highest degree 
of efficiency for classes of a given size would be attained if the 
methods of instruction were selected with particular reference to 
this size of class. It would not be surprising to find that methods 
of instruction which were most effective in small classes would be 
considerably less effective with large classes, and that methods well 
suited to the handling of large classes would not give the best results 
when used with small classes. This possibility was not considered 
in this investigation. Hence, the findings should not be accepted as 
final. There is still need for an investigation in which methods 
of instruction are adapted to size of class. 

Finally, it must be remembered that the problem of the size of 
class is not entirely a problem of the efficiency of the school. It is 
also a problem of the teacher. It is not humane and it is not socially 
profitable to assign teaching loads so heavy that teachers become 
overworked. The problem of the teacher was not considered In this 
investigation. 



CHAPTER II 
EXISTING CONDITIONS IN REGARD TO CLASS SIZE 

In order that the significance of the two investigations to be 
reported in the following chapters may be more fully appreciated, 
certain facts are presented, concerning the size of class under present 
school conditions in Illinois. 

Size of class in elementary schools in Illinois outside of 
Chicago. Data with reference to the size of class in the elementary 
schools of the state, outside of Chicago, were secured by sending a 
questionnaire to the superintendent of public schools in all cities and 
towns listed in the Illinois School Directory for 1920-21 as having 
six or more elementary teachers. The questionnaire asked for the 
number of elementary teachers having classes of the following sizes: 
less than 20, 20 to 29, 30 to 39, 40 to 49, and 50 and over. This 
information was requested for each of the school years of 1918-19, 
1919-20, and 1920-21. Complete reports were received from 180 
cities and towns. These are summarized in Table I. The total 
number of classes for which a report was secured varied from 9,422, 
1918-19, to 10,403, in 1920-21. The median size of class varied from 
41.4 pupils, 1918-19, to 43.3 pupils, in 1919-20. In 1920-21, the size 
of class was slightly less than that for the preceding year. This 
table also shows that, in the cities reporting, slightly more than 3 
percent of all classes contained SO or more pupils. On the other 
hand, between 7 and 8 percent of the classes had less than 30 pupils. 
The greatest change in regard to the size of class during this period 
was in the marked decrease in the number of classes having between 
30 and 39 pupils. During the school year, 1918-19, the size of slight- 
ly more than one-third of the classes fell within these limits. During 
the other two school" years, covered by this study, less than one- 
fifth of the classes came within these limits of size. This change is 
offset by a corresponding increase in the number of classes having 
between 40 and 49 pupils. Although the span of years covered by 
this table is insufficient to justify conclusions with reference to the 
trend of the size of class, Table I suggests that there is a tendency, in 

10 



TABLE I. SIZE OF CLASSES IN THE ELEMENTARY SCHOOLS OF 180 
ILLINOIS CITIES FOR 1918-21. 



Number in 
Classes 


1918-19 


1919-20 


1920-21 


Number 
of Classes 


Percent 
of Classes 


Number 
of Classes 


Percent 
of Classes 


Number 
of Classes 


Percent 
of Classes 


50 


313 

5134 

3264 

598 

113 


3.3 

54.5 

34.6 

6.3 

1.3 


342 

6865 

1845 

646 

110 


3.5 

70.0 

18.8 

6.6 

1.1 


350 

7161 

2050 

719 

123 


3 4 


40-49 

30-39 

20-29 

Less than 20 


68.8 

19.7 

6.9 

1.2 


Total 


9422 


100.0 


9808 


100.0 


10403 


100.00 


Median 




41.4 




43.4 




43.2 



the elementary schools of Illinois outside of Chicago, to assign from 
40 to 50 pupils to a teacher. 

Size of class in Chicago public schools, October, 1920. 

Because the two investigations to be reported later were carried on, 
for the most part, in certain schools in Chicago, it was thought de- 
sirable to compile separately the facts relating to class size in Chi- 
cago. The information was taken from the records of the superin- 
tendent of schools. One-half of the elementary schools were selected 
at random, but all of the high schools were included. Information, 
with reference to the size of class in each grade, is summarized in 
Table II. Below the ninth grade, the classes are noticeably larger 
than in the high school. The median size of class is approximately 
46 pupils. In the high school, a greater degree of variability is 
shown in the size of class. Approximately 14 per cent of the classes 
have fewer than 20 pupils. The median size of class for the high 
school is slightly over 30 pupils. It will be noted that the classes for 
the first year are larger than those for the following years. Of the 
183 classes, 178 reported as having from 50 to 54 pupils, are classes 
in physical training. A number of these have more than 54 pupils. 
The size of high school classes is given by subjects in Table III. 
The median size of class for the different subjects ranges from 20.0, 

11 



TABLE II. SIZE OF CLASSES IN CHICAGO SCHOOLS, OCTOBER, 1920. 



Grades 


Less 
than 








Num 


ber in 


class 








55 
and 


To- 
tal 


Med- 






















ian 




10 


10-14 


15-19 


20-24 


25-29 


30-34 


35-39 


40-44 


45^9 


50-54 


over 






1 






3 


1 


6 


20 


40 


120 


248 


87 


36 


561 


46.8 


2 






1 


2 


1 


6 


11 


102 


247 


38 


1 


409 


46.7 


3 






1 


1 


1 


3 


18 


96 


211 


48 


3 


382 


46.7 


4 








1 


2 


3 


15 


90 


207 


39 




257 


46.6 


5 






1 






2 


4 


79 


215 


48 


1 


350 


47.1 


6 






3 


3 


1 


2 


12 


103 


183 


27 


4 


338 


46.2 


7 










2 


2 


15 


92 


180 


32 


3 


326 


46.4 


8 

1 








1 




4 


54 


79 


117 


15 


48 


318 


44.8 


Total 




























Element 


ary 




9 


9 


13 


42 


169 


761 


1618 


334 


96 


3041 


46.6 


Schools 




























9 


36 


108 


224 


556 


613 


850 


683 


254 


98 


92 




3474 


32.3 


10 


24 


84 


202 


342 


378 


401 


283 


136 


17 


69 




1936 


29.3 


11 


14 


60 


90 


178 


148 


189 


119 


31 


10 


19 




858 


27.8 


12 


15 


27 


64 


67 


81 


93 


77 


29 


2 


3 




458 


28.4 


Total 




























H. S. 


89 


279 


580 


1143 


1220 


1533 


1162 


450 


87 


183 




6726 


30.2 



for German, up to 34.5, for arithmetic. If physical education is in- 
cluded, the maximum median class is 43.8. However, the most sig- 
nificant aspect of the table is the wide variation in the size of class 
for a given subject. With few exceptions, there are, in each subject, 
classes having 10 or less pupils and also classes having more than 
45 pupils. The exceptions are shop work, in which the number of 
pupils is probably limited by the equipment, office practise, of which 
there are only 37 classes in the entire school system, chemistry, home 
economics, botany, zoology and agriculture, in which equipment 
again probably limits the size of class. In German there are no 
classes having more than 34 pupils, but there are only 8 classes in 
the entire system. 

Opinions of city superintendents in regard to the best size 
of class. A questionnaire was sent to the city superintendents of 
public schools in all cities in the United States having a population 



12 



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o^lOTt^osO■*^^no^■*^csvo^^co<N•^cocoool-Hr^coo 

TfCO'-n^U-lTtli-l ^ VOT}<TtlOSr^\004(NW->r-lOCOCNVO 



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i 



i J 2 



vo >o r-~ t-H ,-( r^ 



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. 60 

>- s 

bo JJ 

^ CI, 



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bp g T 



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pQfcii:oH<ci,ouoc^oHjS<a<:mcJoOHj^ii:wo 



TABLE IV. IDEAL SIZE OF CLASSES AS INDICATED BY 270 SUPERINTEND- 
ENTS IN CITIES OF 25,000 OR MORE POPULATION. 







Grades 




Score 










1, 2, 3, 


4, 5, 6, 


7, 8, 9, 


10, 11, 12 


55-59 


1 








50-54 




1 


1 




45-49 


2 


2 




1 


40-44 


16 


18 


15 


2 


35-39 


53 


73 


35 


4 


30-34 


95 


95 


104 


33 


25-29 


52 


42 


58 


95 


20-24 


20 


21 


48 


95 


0-19 


30 


18 


9 


16 


Total 


269 


270 


270 


246 


Median — 


31.7 


32.8 


31.0 


25.6 



of 25,000 or more, as shown by the directory issued by the Bureau 
of Education. The questionnaire asked the superintendents to indi- 
cate the ideal size of class in their opinion for grades one to three, 
four to six, seven to nine, and ten to twelve. Replies from 270 cities 
are summarized in Table IV. One of the most interesting things 
about this table is the wide range of opinion which it indicates. A 
considerable number of superintendents would have fewer than 20 
pupils in each class. Other superintendents appear to consider classes 
of 40 or more ideal. One superintendent indicates that he would 
be satisfied with classes of 55 pupils in the primary grades. The 
ideal median size of class below the high school ranges from 31.0, 
for the junior high school, to 32.8, for the intermediate grades. In 
the senior high school, the ideal median of class is 25.6 pupils. 

The problem of class size. Although Table IV is based upon 
replies from superintendents distributed over the United States, and 
the preceding tables refer to existing conditions in Illinois, we are 
probably justified in pointing out that a marked difference exists 
between theory and practise. The prevailing practise in the elemen- 
tary schools of the state outside of Chicago centers around classes 



14 



having from 40 to 45 pupils. The median ideal size of class is only 
slightly above 30. Thus, it appears that the practical problem in 
which school superintendents are interested relates to a determina- 
tion of the relative efficiency of classes enrolling from 25 to 35 pupils 
as compared with classes enrolling from 40 to 45 pupils. 

For the high school, we have no data relating to the size of 
class in Illinois except for the city of Chicago. The median ideal size 
is approximately 25. The median actual size is approximately 30. 
It, therefore, appears that the practical problem in the high school 
relates to the relative efficiency of classes enrolling from 20 to 30 
pupils as compared to those enrolling from 25 to 35. 



IS 



CHAPTER in 

RELATION OF SIZE OF CLASS IN ELEMENTARY SCHOOL 
TO SCHOOL EFFICIENCY 

General plan of the study in the elementary school. In 

order to study the effect of variations in the size of class upon the 
achievements of pupils, it is necessary to hold constant or to measure 
the other factors which affect their achievements. It was planned 
to keep the teacher constant by having both a large class and a small 
class taught by the same teacher. Since the plan of organization in 
the elementary school makes it impossible for the same teacher to 
instruct two classes at the same time, it was necessary to have a teach- 
er instruct the two types of classes during two consecutive semesters. 
It was arranged to have some of the teachers instruct a large class 
during the first semester and a small class during the second semes- 
ter. Other teachers instructed a small class during the first semester 
and a large class during the second semester.^ 

In order to keep the pupil material as nearly constant as pos- 
sible, "one hundred percent promotion" was secured at the end of 
the first semester in all of the experimental groups. When a teacher 
instructed a large class during the first semester a number of pupils 
were sent to another teacher at the beginning of the second semester. 
The pupils remaining formed a small class. In doing this, an effort 
was made to select pupils so that those remaining would form a 
small class having approximately the same average mental age and 
the same variability of this trait. When a teacher instructed a small 
class during the first semester, pupils were added at the beginning 
of the second semester, but care was exercised to have these pupils 
such that the average mental age of the class would not be materially 
affected. 

This investigation, which began in October, 1920, was confined 
to classes in grades II, V, and VII. Some of the experimental groups 
were organized in the B sections of these grades and the others in 
the A sections- At the beginning of the second semester the B sec- 

^This investigation was carried on in five elementary schools in Chicago: Wash- 
ington, Cleveland, Lowell, Farragut, and Hibbard. 

16 



tions became A sections of the same grade and the A sections be- 
came B sections of the next higher grade. We shall, however, refer 
to the grades simply as II, V, and VII. Data for only those pupils 
who attended both the large class and the small class and who took 
all of the tests given are included in the following tabulations. 

The size of the experimental classes. In the second grade 
there were eleven experimental classes, three small the first 
semester and large the second, and eight of the opposite type. If 
one class, enrolling only 18 pupils when considered a large class, is 
excluded, the small classes range from 33 to 44 and the large from 
45 to 54. The differences in the size of the paired groups range from 
4 to 13, the average being approximately eleven pupils. In the fifth 
grade there were thirteen experimental classes, three small the first 
semester and large the second, and ten of the opposite type. The 
small classes range in size from 33 to 45 and the large from 42 to 
52. The differences in the size of the paired groups range from 4 
to 14, the average difference being approximately 9. In the seventh 
grade there were only five experimental classes, three of one type 
and two of the other. The small classes ranged from 35 to 44 and 
the large from 42 to 49. The average difference in size was approx- 
imately 7. It should be noted that in both the fifth and seventh 
grades there is some overlapping in the size of the two types of 
classes. Some "large classes" are smaller than certain "small classes." 
Data collected. In the second grade, the Dearborn Group In- 
telligence Test and Pressey Primer Scale were given at the begin- 
ning of the experiment. In this grade, achievement was measured 
by giving the Indiana Scale of Attainment, No. 1. Form 1 was given 
in October, Form 2 in January, and Form 1 was used again at the 
end of the year. In grades V and VII, the Illinois General Intelli- 
gence Scale was used. The achievements of the pupils were meas- 
ured in arithmetic, silent reading, language, and spelling. In arith- 
metic and reading, the measurements were secured by means of the 
tests included in the Illinois Examination. Form 1 was used for the 
first and third testings and Form 2 for the second. In language, 
Charters' Diagnostic Language Test for pronouns was used. Form 
1 was given in October and in May. Form 2 was used for the Jan- 
uary testing. In spelling, 20 words were selected from columns N 
and R of the Buckingham Extension of the Ayres' Spelling Scale. 

17 



For the first and third testings, the words were selected by beginning 
at the bottom of these columns and choosing alternate words. The 
words for the second testing were taken from these columns, begin- 
ning with the next to the last word and taking alternate ones. 

Administration of tests and collection of data. All the tests 
were administered and scored by the teacher. As a preparation for 
this work, the teachers were called together and given definite in- 
structions concerning the nature of the tests and the plan of admin- 
istration. In this connection, the tests were administered to the 
teachers in order to illustrate to them the procedure to be used with 
the pupils. All of the tests are highly objective with reference to the 
scoring, and samplings of the test papers failed to reveal any large 
errors in this work. The teachers reported the data for each pupil 
on an individual record card. This card contained spaces for each 
score and each test as well as for data with reference to the size of 
class in which the pupil was taught during each semester. The 
dates of testing were approximately as follow: October 20th, Feb- 
ruary 20th, and May 20th. 

Method of summarizing the data. The data summarized 
were limited to the scores of only those pupils who were members 
of both a large class and a small class, and who were present at all 
three testing periods. The scores of all pupils in a grade (including 
both A and B sections), who had been taught in the same type of 
class, were assembled for each of the three testings. For example, 
the October arithmetic scores for all fifth grade pupils who were 
taught in large classes during the first semester and in small classes 
during the second semester were assembled in one distribution. An- 
other distribution was made for the January scores and a third one 
for the May scores. Three corresponding distributions were made 
for the arithmetic scores of the pupils who were taught in small 
classes during the first semester and in large classes during the sec- 
ond. Thus, there were obtained six distributions for each achieve- 
ment score. One measure of the gain in achievement made by a 
group of pupils during the first semester was found by subtracting 
the average of the October scores from the average of the January 
scores. Another measure of the gain was found by subtracting the 
median October score from the median January score. In a similar 
manner, the gains for the second semester were obtained by sub- 

18 



tracting the average and the median January scores from the cor- 
responding May scores. 

In calculating these gains, no account was taken of the possible 
non-equivalence of the different forms of the tests used. In fact, 
no accurate information concerning the equivalence of the duplicate 
forms is available, except for the tests in reading and arithmetic. 
The duplicate forms of these two tests have been shown to be ap- 
proximately equal,^ Since Form 1 was used twice, and the average 
and the median scores calculated from it were used both as subtra- 
hends and minuends, any non-equivalence of the forms will not af- 
fect the comparisons of gains made in the following table. 

The scores of the different tests are expressed in terms of dif- 
ferent units. Thus, before any combination of the results from the 
different tests can be made, it is necessary to express the gains in 
terms of a common unit. The usual assumption in such cases is that 
the standard deviation of the distribution of scores represents the 
same increment of ability for one test and in one grade as in another. 
On the basis of this assumption, the stardard deviation was calcu- 
lated for six of the different distributions of scores for each test in 
a given grade, and the average of these six standard deviations was 
used as a divisor to reduce the gains to a basis of a common unit. 
For example, during the first semester the fifth grade pupils taught 
in large classes in arithmetic made a gain of 12.0 points.^ During 
the second semester they made a gain of 7.2 points. The gains for 
the pupils taught in small classes in arithmetic were 6.5 and 5.65. 
The average standard deviation of the six distributions of arithmetic 
scores is 17.441. Dividing these gains by this average standard de- 
viation, we secure as quotients the entries (.68, .41, .36, and .32) to 
be found In Table V. 

In calculating the average gains for the two types of classes, 
the simple average of the two gains has been used rather than the 
weighted average, although the two groups are not even approxi- 
mately equivalent in size. Since our purpose in taking this average 
is to eliminate any differences In the course of study or In the edu- 



"Monroe, Walter S. "The Illinois Examination." University of Illinois Bulle- 
tin, Vol. 19, No. 9, Bureau of Educational Research Bulletin, No. 6. Urbana: Uni- 
versity of Illinois, 1921. 

'These gains were calculated from the average of the scores. 

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cational opportunities offered in the two semesters and also any 
practise effect due to acquaintance with the tests, it seemed unwise 
to weight the averages on the basis of the number of pupils in the 
two groups. To have used the weighted averages in this case would 
have resulted in giving greater weight to the gains made by one 
group of pupils simply because this group happened to be larger. 

Achievements of the two groups approximately equal. 
Table V* summarizes the data with reference to the gains made by 
the two groups. The column headed "Number of pupils" gives the 
number of pupils whose records were used in the tabulations. (A 
pupil's record was discarded if he was not a member of both the 
small class and the large class and if he did not take all tests.) The 
average size of class is computed from the total enrollment. The 
computation of the gains has just been explained. In interpreting 
the table, attention should be focused upon the differences. A posi- 
tive difference means that the large class is superior in achievement, 
and a negative difference that the small class is superior. At the 
bottom of each difference column the differences, calculated from 
the averages and also from the medians, are summarized. This 
summary is a total and not an average. To find the average it is 
necessary to divide by 3. All of the totals of the differences fall 
between 4-1.00 and —1.00. Six of the 10 differences are negative, 
and only in the case of reading rate are the difference between the 
averages and the difference between the medians both positive. In 
the last three columns of the table. We have the totals and not aver- 
ages. To find the average, it would be necessary to divide by 4 in 
the second grade and by 5 in each of the other two grades. Here, 
again, the negative differences predominate, although none of them 
are very large. The last two entries in the last column are essentially 
grand totals and may be considered to summarize the entire table. 
To find the average difference, each of these numbers should be di- 
vided by 14. The quotients obtained would be — .04 and — .06. 
Thus, in general, this table indicates that there is little if any superi- 
ority in the achievements of pupils in the small classes over those 
of pupils in the larger classes. 



*The entries in the column headed "Reading Rate" in the second grade are 
based upon the Pressey Word Recognition Test. 

21 



An examination of Table V reveals the fact that, in general, the 
gains between the first and second testings are much larger than 
those between the second and third testings. This condition em- 
phasizes the necessity for equalizing the effect of acquaintance with 
the test and practise effect. If all of the experimental groups had 
been taught as large classes the first semester and small classes the 
second, the gains for the large classes would greatly exceed the gains 
for the small classes; but this would be due primarily to the effect 
of acquaintance with the test and the practise effect. 

When Table V is examined with reference to the conditions in 
the different grades we find that the gains are relatively greater for 
the small classes in the fifth grade than in either the second or the 
seventh grade. However, the number of pupils is so small for the 
two groups in the seventh grade and the groups differ so little in size 
that only slight significance can be attached to the results. Even in 
the second and fifth grades it is unfortunate that the experimental 
groups are not more nearly equal in size. It is possible that if the 
experiment had included a larger number of classes which were small 
the first semester and large the second different results might have 
been obtained. 

When the gains for the different subjects are examined we find 
that in language the gains for the small classes are consistently 
greater than the gains for the large classes. This is not true for any 
other subject. Although in spelling the total of the gains is distinctly 
negative, in both arithmetic and reading comprehension the total 
when computed by one method is negative and in the other case is 
approximately 0. Reading rate in the seventh grade is the only case 
in which the large class is distinctly superior in achievement. 

Conclusion: the relation of the size of class to school efl5> 
ciency. Since Table V indicates that, on the whole, there is little 
difference between the achievements of the pupils when taught in 
large classes and their achievements when taught in small classes, 
one might infer that the efficiency of a school would be materially 
increased by the formation of large classes, because the educational 
output would be approximately the same and the educational invest- 
ment would be materially decreased. However, it is doubtful that 
the present investigation justifies such a conclusion. In the first 
place, it is obvious that only certain achievements of pupils have 

22 



been measured. Even in the fields of the four subjects in which tests 
were given we are not justified in claiming that all achievements of 
the pupils were measured. The arithmetic tests used were confined 
to the operations and to only certain types of examples within this 
division of arithmetic. In silent reading, the test used Is very limited 
in scope. Similarly, the tests in language and spelling possess very 
definite limitations with respect to scope. There is some justification 
for assuming that the measurements made may be considered in- 
dices of the total achievements of the pupils not only in the fields 
of the four subjects in which the tests were given but also in the 
field of instruction in the grades concerned. However, the thesis 
that the measures of achievement secured in this investigation are 
indices of the total achievement is largely an assumption, and in in- 
terpreting the results it is necessary to recognize this fact. It is 
possible that, if other tests had been used or if the achievements of 
•the pupils had been more completely measured by including tests 
in other subjects, the results might have been different. 

In the second place, it must be remembered that the size of the 
"small classes" was not less than 33 (with one exception), and in a 
few cases the enrollment was as much as 44 or 45. The large classes 
ranged in size from 42 to 54. The average difference between the 
pairs of experimental groups ranged from 7 in the seventh grade to 
11 in the second grade. These conditions with reference to the size 
of the experimental groups constitute a very significant limitation of 
the investigation. One is not warranted in making inferences from 
the facts of Table V with reference to the relative efficiency of classes 
of 20 to 25 pupils as compared with classes of 35 to 45 pupils. No 
application should be made except within the limits of size defined 
by the experimental groups. 



23 



CHAPTER IV 

RELATION OF SIZE OF CLASS IN HIGH SCHOOL 
TO SCHOOL EFFICIENCY 

General plan of the study in the high school. In the inves- 
tigation in the high school it was arranged to have both a large class 
and a small class in a given subject instructed by the same teacher 
during the same semester. This made it necessary to restrict the 
experiment to teachers who were instructing two or more sections 
of the same subject. When a teacher was instructing two sections, 
pupils were shifted on the basis of their intelligence scores so that 
the average quality of pupil material was approximately the same 
in the two sections. Thus, both classes would include some bright, 
some medium, and some dull pupils. When a teacher had four 
sections of the same subject, the pupils were shifted so that a large 
class and a small class would be obtained, consisting of relatively 
bright pupils. The less capable pupils were also divided into two 
classes, one large and one small. 

In establishing the two types of class, there was considerable 
variation in the size of both the large classes and the small classes. 
The small classes varied in size from 12 to 26 pupils. The large 
classes varied in size from 23 to 45 pupils. The average size of the 
large classes was 36.5 and that of the small classes, 20.8. The dif- 
ferences in the size of the paired classes ranged from 6 to 26. 

Source of data. This study was carried on in four large high 
schools in Chicago and in the high schools of three other Illinois 
cities.^ During the first semester of 1920-21, the experiment was 
carried on in beginning tenth grade classes. During the second 
semester of that year the study was confined to classes completing 
the first year of high school work. In the following tables no dis- 
tinction is made between classes for the two grades. Records were 
secured for 67 pairs of classes, enrolling 3,821 pupils. The project 

*The high schools in Chicago were Lane Technical, Tilden Technical, Harrison 
Technical, and Hyde Park. The three other Illinois cities were Macomb, Shelby- 
ville, and West Aurora. 

24 



was begun by giving the Terman Group Test of Mental Ability to 
all pupils concerned, about October 15, 1920. Some pupils in the 
high schools outside of Chicago were given the Illinois General In- 
telligence Scale or the Chicago Group Intelligence Test. As soon 
as the results of the testing could be assembled, the large classes 
and small classes were arbitrarily formed, following the method in- 
dicated above. 

The educational output, or the achievements of the pupils, was 
measured by requiring each teacher to give the same final examina- 
tion to both types of classes. A check upon this measurement of 
achievement was secured by using the "term grades" of the pupils. 
It is generally recognized that "term grades," as well as examina- 
tions set by teachers, are highly subjective. However, in this case 
the same teacher administered the same examination to both the 
small class and the large class. The same teacher also gave the 
"term grades." Thus, there is in no place a comparison between 
either "term grades" or "examination grades" given by different 
teachers. This tends to eliminate the subjective factor of these 
measures. In addition. It may be noted that we are concerned with 
the average "grades" of relatively large groups of pupils and not 
with the "grades" of individual pupils. 

A limitation. The plan of carrying on the experiment implies 
the assumption that the achievements of the, pupils in the large 
classes were equal to the achievements of the pupils in the small 
classes at the beginning of the experimental period. There was no 
attempt to measure the achievements of pupils In the subjects con- 
cerned at the beginning of the experiment. In the first semester, the 
two types of classes were not organized until after the high schools 
had been In session several weeks. In the case of the classes used 
during the second semester, the pupils had received an entire semes- 
ter of Instruction in regular classes. It is true that the sections 
were formed so that the average general intelligence of the paired 
classes was approximately equal, but this probably does not justify 
the assumption of equivalent achievements. 

Details of administration. The Intelligence tests were admin- 
istered and scored by the teachers. As preparation for this work, 
the teachers were called together and given definite Instructions con- 
cerning the nature of the tests. The tests were also administered 

25 



to them. They were then required to score their own papers. All 
the tests used were highly objective with reference to scoring, and 
a sampling of the test papers of the pupils failed to reveal any large 
errors in this work. Since, in the use of the intelligence test scores, 
comparisons are always made between the pupils or groups of pupils 
under the same teacher, variations in the administration of the tests, 
due to dijfferences between teachers, would not be significant. 

At the close of each semester the teachers were asked to report 
both the "final grade" and the "examination grade" for each stu- 
dent.^ In most cases, the "examination grades" were reported in 
terms of percents. The "final grades" were generally reported in 
terms of letters, as follow: 

S==Superior 

E=Excellent 

G=Good 

F=Fair 

D=Failure 

For the purpose of combining "grades," these letters were as- 
sumed to represent the following numerical ranges on a scale of 100 
percent: 

S is equivalent to 95 and over 

E is equivalent to 85 to 94 

G is equivalent to 75 to 84 

F is equivalent to 65 to 74 

D is equivalent to 55 to 64^ 
Plan of summarizing data. The data collected were sum- 
marized to show the differences, if any, which existed between the 
final achievements of pupils in the large classes and of pupils in the 
small classes. Two methods of summarizing were employed. In 
the first, the achievements of all pupils were considered. According 
to the second method, the records considered were limited to those 
of pupils in the large classes who could be paired with pupils having 
identical scores on the intelligence test in the corresponding small 

The following tables, in which the data for high school classes are summarized, 
indicate that the "examination grades" were not received from certain classes. 

°The midpoints of these intervals were presumably used as the numerical equiv- 
alents of the grades expressed in terms of letter. However, Mr. Stevenson's report 
yields no information on this point. 

26 



classes. For both of these methods two tabulations have been made. 
The first includes all classes, and the second only those pairs of 
classes in which the large class was at least twice the size of the small 
class. 

Differences in achievements when all pupUs are consid' 
ered. Table VI illustrates the first method of summarizing the data 
for 22 pairs of English classes. In the second and third columns 
of this table the enrollment in the large classes and in the small 
classes is given. The quantities recorded in the three columns headed 
"Difference" are found by subtracting the quantities in the two col- 
umns immediately preceding the difference column. The number 
for the small class is, in every case, taken from that for the large. 
Therefore, a positive difference means that the large class is superior 
in the trait concerned, and a negative difference, that the small class 
is superior. The line at the bottom of the table gives the average 
for each column. These averages may be taken as summarizing the 
data collected from these 22 pairs of Enghsh classes, although the 
items combined are not entirely comparable. For example, different 
general intelligence tests were used in different classes. The present 
writer has not been able to ascertain the particular intelligence test 
given to any pair of these 22 pairs of classes. It is, however, difficult 
to explain the extreme differences between the average intelligence 
scores of classes 10 and 11 on any basis other than the use of different 
tests in these two pairs of classes. Furthermore, it is not unlikely that 
different passing marks are in use in the different schools in which the 
pairs of classes were taught. If this is the case, in the case of differ- 
ent pairs of classes, both the average term grades and the average 
examination grades are on different scales. 

It should be noted that, although an effort was made to organ- 
ize a large class and a small class so that the average intelligence 
scores would be approximately the same for the two classes, this was 
not always accomplished. Because of conflicts or other conditions 
that could not be disregarded, it was not always possible to shift pupils 
from one section to the other so as to set up the desired class organ- 
ization. 

Table VII summarizes the averages for the classes in the dif- 
ferent subjects. In interpreting this table, it is necessary to bear in 
mind that, with the exception of English and algebra, the number of 



27 



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result representative. Certainly, little if any significance can be at- 
tached to the results for Latin, history, and French. The average 
for the 67 pairs of classes is the weighted average, so that one pair 
of classes does not influence this average any more than any other 
pair. 

Table VIII presents a summary for those pairs of classes in 
which the large class is at least twice the size of the small class. By 
doing this, we are able to examine the achievements of pupils in 
pairs of classes where the difference in size is marked. The number 
of classes in any one school subject is so small, with the exception 
of English, that we are probably not justified in drawing any conclu- 
sions for the separate subjects. 

Diflferences in the achievements of paired pupils. Table IX 
is similar to Table VII, the only difference being that it is based 
upon the records of only those pupils in the large classes who could 
be paired with pupils in the corresponding small classes, having the 
same scores on the general intelligence test. Since the pupils were 
paired on the basis of their intelligence scores, the average general 
intelligence of those taken from the large classes would be identical 
with the average general intelligence of those taken from the corre- 
sponding small classes. Hence, the average general intelligence 
scores are omitted. Table X is similar to Table VIII. 

Interpretation of the tables. When all 67 pairs of classes 
are considered, the average of the general intelligence scores for the 
large classes is almost identical with that for the small classes, the 
difference being only one-tenth of a unit. This unit corresponds 
approximately to one month of mental age. We may, therefore, 
consider the pupils in the large classes equal in general intelligence 
to the pupils in the small classes. Both the average "term grade" 
and the average "examination grade" are slightly larger for the small 
classes. 

The question of the significance of the diff'erence of two aver- 
ages is involved here. Both examination grades and final grades 
are known to be highly subjective and to involve a large error which 
is a combination of a constant error and a variable error. Variable 
errors tend to offset each other in an average because some of them 
are negative and some positive. On the other hand, constant errors 

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are not eliminated in averages. The number of pupils included in 
the 67 pairs of classes is sufficiently large so that the average grades 
include a variable error which is probably so small as to be negli- 
gible. For example, if we assume that the probable variable error 
of a grade is as much as 10 points, which is probably in excess of 
the actual probable variable error, the probable variable error of the 
average for the small classes would be less than three-tenths of one 
point. In the case of the large class, it would be materially less than 
in the small class. The constant errors, which are expressed in the 
tendency of some teachers to give higher grades than others, are 
probably included in both groups in approximately the same pro- 
portion, since the same teacher assigned grades to bpth a small class 
and a large class. If this is true, a difference of 1.3 between the 
average term grades is probably significant, although there is a 
reasonable doubt. This doubt is materially increased and probably 
the difference loses its significance when we recall that the achieve- 
ments of the two groups of students were not measured at the be- 
ginning of the experimental period. 

When we consider the summaries for the different subjects, we 
find the differences between the average achievements of the pupils in 
the two types of classes materially larger in a number of cases than 
the differences between the averages for the 67 pairs of classes. How- 
ever, in interpreting these differences it is necessary to remember 
that the number of pupils is materially less and, hence, a difference 
must be materially greater in order to be significant. It is perhaps 
significant that negative differences predominate. This suggests that 
the average achievements in the small classes are somewhat superior 
to those in the large classes, but in drawing conclusions from this 
condition it is necessary to bear in mind the fact that the achieve- 
ments of the students were not measured at the beginning of the 
experimental period. 

When we turn to Table VIII, which is restricted to those classes 
in which the large class is at least twice the size of the small class, 
we find that the pupils in the small classes were slightly superior in 
general intelligence. If the size of class is a potent factor in de- 
termining the achievements of pupils, we should naturally expect to 
find a greater difference in the achievements of the two types of 
classes than we found in Table VIII. The fact that the difference 

34 



is less, both absolutely and relatively, suggests that the size of class 
is not a potent factor in determining the achievements of pupils. 
However, the number of pairs on which Table VIII is based is so 
small that no great importance should be attached to this observa- 
tion. 

When we examine Table IX, we find that the differences be- 
tween the averages for the 67 pairs of classes are only slightly larger 
than those given in Table VII. In general, there are few significant 
differences to be noted in a comparison of these two tables. One of 
the most significant is the reversal of the relative achievements of 
the large class and the small class in Latin. In Table VII, when all 
pupils were considered, those taught in the large class were shown 
to be distinctly superior in achievement. When only the paired 
pupils were considered, those taught in the small class were dis- 
tinctly superior in achievement. Considering the table as a whole, 
we are justified in asserting that it tends to corroborate the interpre- 
tations suggested for Table VII.* 

Conclusion: relation of size of class in high school to 
school efficiency. The tables of this chapter show that at the end 
of the experimental period the achievements of the students in the 
two types of classes were approximately equal, and there is a slight 
indication that those taught in small classes were superior. Since 
the educational investment can be materially decreased by increas- 
ing the size of class in the high school, one might infer that the effi- 
ciency of the school would be increased by organizing classes enroll- 
ing from 35 to 40 students instead of classes enrolling from 20 to 25. 
In addition to the fact that there are several uncontrolled factors 
whose influence is unknown, it is necessary to bear in mind the exact 
conditions of the experiment. Since the same teachers taught both 



^In his report, Mr. Stevenson attempted the further analysis of the data by 
ascertaining the percent of pairs of pupils in which the pupil in the small class re- 
ceived a higher grade than the corresponding pupil in the large class. When all 
pairs of pupils are considered, he shows that only in 40 percent of the pairs does 
the pupil in the small class surpass his mate in the large class. However, it is 
impossible to draw any conclusion from this fact, because we do not know the per- 
cent of pairs in which the two pupils received the same mark. Since, in a majority 
■of the cases, the grades were reported in terms of letters and only five marks were 
recognized, it is reasonable to expect that in a relatively large percent of the cases 
both of the paired pupils received the same final grade. 

35 



a small class and a large class, there was no difference between the 
total amount of work done by the teachers who handled the large 
classes and the teachers who handled the small classes. In fact, they 
were the same teachers. Thus, this experiment failed to set up the 
conditions of large classes as a general plan of organization of a high 
school. It did, however, realize the conditions which not infrequently 
exist in the smaller high schools where it is desirable to have a few 
large classes assigned to teachers who are given compensating small 
classes or who have the number of classes reduced accordingly. The 
results of the experiment, therefore, can be applied only to those 
situations in which the teaching load is kept constant. In such cases 
the evidence collected indicates that approximately the same aver- 
age achievement can be expected from the pupils taught in large 
classes as from those taught in small classes. In other words, the 
results of this experiment indicate that there is no loss of efficiency 
caused by organizing a few large classes if the other work assigned 
to the teacher is such that the teaching load is not increased. 

One should recognize that the results of this experiment should 
not be applied to the question of the size of class where increasing 
the size of class results in a distinct increase in the teaching load. 
The instruction which students receive is given partly in the class 
room and partly through written work and individual conferences. 
In such subjects as English composition, algebra, and science re- 
quiring laboratory work, it is customary with most teachers to re- 
quire a large amount of written work. A teacher who gives instruc- 
tion to five classes of 40 students each has a much heavier teaching 
load than the teacher who instructs five classes of 20 students each, 
unless he introduces compensating changes in the amount of written 
work, in the method of handling it, and in the number of individual 
conferences. In such cases the question of class size is so intimately 
connected with the method of instruction that we are not justified 
in drawing any inferences from an investigation in which the method 
of instruction was assumed to be the same for both types of classes. 



36 



CHAPTER V 
SUGGESTIONS FOR EDUCATIONAL EXPERIMENTATION^ 

The two studies described in Chapters III and IV make very 
sHght contributions to a scientific determination of the relation be- 
tween the size of class and the efficiency of a school system. They 
do, however, seem to the writer of this chapter suggestive with ref- 
erence to the procedure of educational experimentation. The causes 
of the failure of these studies to produce reliable and significant re- 
sults have been mentioned in the two preceding chapters but they 
may be summarized under two general heads: first, failure to set 
up and maintain appropriate experimental conditions and, second, 
the lack of adequate instruments for measuring the achievements of 
pupils. 

A prerequisite for setting up and maintaining appropriate ex- 
perimental conditions is a complete analysis of the problem being 
studied. The various factors involved must be recognized by the 
experimenter and the possibility of any relations which may exist 
between these factors must also be considered. For example, in the 
high school many factors contribute to the achievements of students, 
or the educational output of the school. In addition to the size of 
class, which is the factor whose relationship to school efficiency was 
studied, it is necessary to recognize methods of instruction, the per- 
sonality and enthusiasm of the teacher, the discipline of the class 
and of the school, the general spirit of the school, the general atti- 
tude of the community toward the school, the time of day when the 
class recites, the textbooks used, the equipment, including the build- 
ing, the "spiritual composition" of the class, the general intelligence 
of the students, their nationality, their past experience, both in school 
and out of school, the stage of advancement reached in their educa- 
tion, and possibly even other factors. It appears likely that certain 
of these factors are interrelated. The size of class is likely to affect 
the enthusiasm of the teacher, particularly if it determines the in- 

^This chapter has no counterpart in the report submitted by Mr. Stevenson. It 
is entirely the contribution of the present director of the Bureau of Educational 
Research. 

37 



structlonal load carried by the teacher. It also appears that some 
relationship exists between the size of class and methods of instruc- 
tion, and between the size of class and discipline. The ex- 
istence of a functional relationship between two or more factors 
makes it impossible under normal conditions to produce variations 
in one factor without, at the same time, causing changes in the others. 
Failure to analyze the problem sufficiently will frequently cause the 
results of an educational experimentation to have little significance, 
and consequently the time and money invested in the study will be 
largely wasted. 

When one considers the total product of the educational pro- 
cess one cannot fail to become impressed with the inadequacy of our 
present educational tests as instruments for the measurement of the 
various elements of this product. In the study relating to the size 
of class in the elementary school a more elaborate group of tests 
might have been used, but even if this had been done, it does not 
appear likely that one would be justified in asserting that the total 
product of education had been measured. In the high school no 
standardized educational tests were used. It was attempted to have 
the achievements measured by means of a final examination and by 
the term "grade" given to the students. The writer of this chapter 
is not aware of the considerations which resulted in the decision not 
to use any of the standardized educational tests that have been de- 
vised in the field of high school subjects, but it is likely that this de- 
cision was due to the belief that none of the available educational 
tests were sufficiently satisfactory measuring instruments to justify 
their use in this investigation. The present writer is inclined to share 
this belief. Thus, we cannot escape the conclusion that at the pres- 
ent time we do not have available instruments for measuring the 
outcomes of teaching which permit reliable educational experimenta- 
tion when it is necessary to measure the total product of instruction. 

Incidentally, attention may be called to the fact that more con- 
sideration should be given to the errors involved in the data and to the 
effect of these errors upon the results of statistical calculations. For 
example, it is highly important to know what significance should be 
attached to a difference between two averages. 

In view of the difficulties encountered in setting up and main- 
taining appropriate experimental conditions and in view of the im- 

38 



perfections and limitations of our present educational tests, it is 
not inappropriate to question the wisdom of undertaking such com- 
plex educational experimentation as has been described in this mon- 
ograph. It is true that there are many educational problems which 
are highly important. For example, an increase in the size of class 
would result in a material reduction in the educational expenditures 
for instruction. A reliable scientific determination of the relation- 
ship existing between the size of class and school efficiency would 
be a valuable contribution, but it is doubtful whether such a deter- 
mination of this relation is at the present time possible. 

To the present writer, it appears highly important that those 
engaged in educational research should give very careful considera- 
tion to the sort of problems to which they devote their energies. 
It is, of course, necessary that pioneer work be done, and in studies 
of this type, it is not always possible to anticipate the limitations 
of one's procedure. As a result it may become necessary to "scrap" 
a project because of the defects that appear in the course of one's 
work. Such losses are unavoidable in extending the frontiers of ed- 
ucational research. When an investigation is not pioneer work an 
experimenter should determine the limitations of his procedure in 
advance, and unless it appears likely that information of considerable 
value will be secured in spite of the limitations the investigation 
should not be undertaken. The fact that a problem is important 
does not justify its study. Educational experimentation which in- 
volves the use of faulty method and faulty instruments not only 
fails to make adequate contributions to our educational progress, 
but, more important, it tends to reflect unfavorably upon the ap- 
plication of the methods of research to the field of education. 



39 



THE UNIVERSITY OF ILLINOIS 

THE STATE UNIVERSITY 
URBANA 

DAVID KINLEY, Ph.D., LL.D., President 



The University Includes the Following Departments 

The Graduate School 

The College of Liberal Arts and Sciences (Ancient and Modern Languages 
and Literatures; History, Economics, Political Science, Sociology, Philosophy, 
Psychology, Education; Mathematics; Astronomy; Geology; Physics; Chemistry; 
Botany, Zoology, Entomology; Physiology, Art and Design) 

The College of Commerce and Business Administration (General Business, 
Banking, Insurance, Accountancy, Railway Administration, Foreign Commerce; 
Courses for Commercial Teachers and Commercial and Civic Secretaries) 

The College of Engineering (Architecture; Architectural, Ceramic, Civil, Elec- 
trical, Mechanical, Mining, Municipal and Sanitary, Railway Engineering, and 
General Engineering Physics) 

The College of Agriculture (Agronomy; Animal Husbandry; Dairy Husbandry; 
Horticulture and Landscape Gardening; Agricultural Extension; Teachers' 
Course; Home Economics) 

The College of Law (Three-year and four-year curriculums based on two years 
and one year of college work respectively) 

The College of Education 

The Curriculum in Journalism 

The Curriculums in Chemistry and Chemical Engineering 

The School of Railway Engineering and Administration 

The School of Music (four-year curriculum) 

The Library School (two-year curriculum for college graduates) 

The College of Medicine (in Chicago) 

The College of Dentistry (in Chicago) 

The School of Pharmacy (in Chicago; Ph.G. and Ph.C. curriculums) 

The Summer Session (eight weeks) 

Experiment Stations and Scientific Bureaus: U. S. Agricultural Experiment 
Station; Engineering and Experiment Station; State Laboratory of Natural 
History; State Entomologist's Office; Biological Experiment Station on Illinois 
River; State Water Survey; State Geological Survey; U. S. Bureau of Mines 
Experiment Station. 

The library collections contain May 1, 1922, 523,230 volumes and 120,151 pam- 
phlets. For catalogs and information address 

THE REGISTRAR 

Urbana, Illinois 



LIBRARY OF CONGRESS 



029 



456 297 7 ^ 



BULLETINS OF THE BUREAU OF EDUCATIONAL RE- 
SEARCH, COLLEGE OF EDUCATION, UNIVERSITY 
OF ILLINOIS, URBANA, ILLINOIS. 

Prite. 

No. I. Buckingham, B. R. Bureau of Educational Research, 

Announcement, 1918-19 15 

No. 2. First Annual Report 25 

No. 3. Bamesberger, Velda C. Standard Requirements for 

Memorizing Literary Material 50 

No. 4. Holley, Charles E. Mental Tests for School Use. 

(Out of print) 50 

No. 5. Monroe, Walter S. Report of Division of Educational- 
Tests for 1919-20 .25 

No. 6, Monroe, Walter S. The Illinois Examination 50 

No. 7. Monroe, Walter S. Types of Learning Required of 
Pupils in the Seventh and Eighth Grades and in the 
High School 15 

No. 8. Monroe, Walter S, A Critical Study of Certain Silent 

Reading Tests 50 

No. 9. Monroe, Walter S. Written Examinations and Their 

Improvement. (In -preparation) 50 

No. 10. Bureau of - Educational Research. Relation of Size 

of Class to School Efficiency 5° 



